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A simple, robust and powerful test of the trend hypothesis

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  • David I. Harvey,
  • Stephen J. Leybourne,
  • A. M. Robert Taylor

Abstract

In this paper we develop a simple test procedure for a linear trend which does not require knowledge of the form of serial correlation in the data, is robust to strong serial correlation, and has a standard normal limiting null distribution under either I(0) or I(1) shocks. In contrast to other available robust linear trend tests, our proposed test achieves the Gaussian asymptotic local power envelope in both the I(0) and I(1) cases. For near- I(1) errors our proposed procedure is conservative and a modification for this situation is suggested. An estimator of the trend parameter, together with an associated confidence interval, which is asymptotically efficient, again regardless of whether the shocks are I(0) or I(1), is also provided.

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File URL: http://www.nottingham.ac.uk/economics/grangercentre/papers/06-01.pdf
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Bibliographic Info

Paper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 06/01.

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Date of creation: Sep 2006
Date of revision:
Handle: RePEc:not:notgts:06/01

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Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
Phone: (44) 0115 951 5620
Fax: (0115) 951 4159
Web page: http://www.nottingham.ac.uk/economics/grangercentre/
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Related research

Keywords: Linear trend; strong serial correlation; asymptotic normality; power enveloope; unit root tests; stationarity tests;

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References

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  1. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, Econometric Society, vol. 66(1), pages 123-148, January.
  2. Perron, Pierre, 1988. "Trends and random walks in macroeconomic time series : Further evidence from a new approach," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 297-332.
  3. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  4. Jansson, Michael, 2004. "Stationarity Testing With Covariates," Econometric Theory, Cambridge University Press, vol. 20(01), pages 56-94, February.
  5. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 124(1), pages 187-201, January.
  6. Bunzel, Helle & Vogelsang, Timothy J., 2005. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 23, pages 381-394, October.
  7. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
  8. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
  9. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, Econometric Society, vol. 56(6), pages 1333-54, November.
  10. Muller, Ulrich K., 2005. "Size and power of tests of stationarity in highly autocorrelated time series," Journal of Econometrics, Elsevier, Elsevier, vol. 128(2), pages 195-213, October.
  11. Faust, Jon, 1996. "Near Observational Equivalence and Theoretical size Problems with Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 12(04), pages 724-731, October.
  12. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, Econometric Society, vol. 69(6), pages 1519-1554, November.
  13. Eugene Canjels & Mark W. Watson, 1994. "Estimating Deterministic Trends in the Presence of Serially Correlated Errors," NBER Technical Working Papers 0165, National Bureau of Economic Research, Inc.
  14. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers, Michigan State - Econometrics and Economic Theory 8905, Michigan State - Econometrics and Economic Theory.
  15. Sun, Hongguang & Pantula, Sastry G., 1999. "Testing for trends in correlated data," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 87-95, January.
  16. Lutz, Matthias G, 1999. "A General Test of the Prebisch-Singer Hypothesis," Review of Development Economics, Wiley Blackwell, Wiley Blackwell, vol. 3(1), pages 44-57, February.
  17. Benedikt M. Pötscher, 1999. "Lower Risk Bounds and Properties of Confidence Sets For Ill-Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation, Unit Roots,and Estimation of Long Memory Paramet," Vienna Economics Papers, University of Vienna, Department of Economics 0202, University of Vienna, Department of Economics.
  18. Mickael Salabasis & Sune Karlsson, 2004. "Seasonality, Cycles and Unit Roots," Econometric Society 2004 Australasian Meetings 268, Econometric Society.
  19. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 64(4), pages 813-36, July.
  20. Grilli, Enzo R & Yang, Maw Cheng, 1988. "Primary Commodity Prices, Manufactured Goods Prices, and the Terms of Trade of Developing Countries: What the Long Run Shows," World Bank Economic Review, World Bank Group, World Bank Group, vol. 2(1), pages 1-47, January.
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